Real-Valued MUSIC Altimetry Method for Meter-Wave Polarimetric MIMO Radar Based on Matrix Reconstruction

Abstract

The present invention discloses a real-valued MUSIC height measurement method for meter-wave polarization MIMO radar based on matrix reconstruction. Aiming at the characteristics of the height measurement signal model of meter-wave polarization MIMO radar and the good decoherence ability of matrix reconstruction technology, a singular value decomposition real-valued MUSIC height measurement method based on matrix reconstruction is proposed. For the meter-wave polarization MIMO radar, first, the corresponding flat ground signal model is derived; then, matrix reconstruction is performed on the received data matrix to eliminate the influence of multipath coherent signals on height measurement; then, the unitary matrix is used to convert the reconstructed data matrix into a real-valued matrix; in order to reduce the influence of noise on the signal subspace and reduce the data dimension, the singular value decomposition technology is applied to the received signal data; finally, according to the principle that the signal subspace is orthogonal to the noise subspace, the target elevation angle value and height value are estimated. The method proposed by the present invention does not require prior knowledge such as known reflection coefficients, wave path differences, and polarization information. Finally, simulation experiments show that the present invention has good accuracy and robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of radar, and particularly to a real-valued MUSIC height measurement method for meter-wave polarization MIMO radar based on matrix reconstruction. Background Art

[0002] Currently, most existing radars are single-polarization array radars, such as MIMO radars, which can only receive one polarization information of electromagnetic wave signals. While vector sensor radars, i.e., polarization radars, have the characteristic of polarization diversity and can obtain at least two polarization information of electromagnetic wave signals or even six polarization information.

[0003] However, there are serious multipath signals in the low elevation angle region of polarization MIMO radars, which seriously affect the height measurement accuracy. In order to make full use of the advantages of polarization MIMO radars, a polarization smoothing generalized MUSIC algorithm is proposed based on the generalized MUSIC algorithm in the prior art. Compared with the generalized MUSIC algorithm of meter-wave MIMO radars, its height measurement accuracy has been improved. Based on the Multiple Signal Classification (MUSIC) algorithm, Zheng proposed the SVS MUSIC algorithm and the generalized MUSIC algorithm for polarization meter-wave MIMO radars, which make full use of the waveform diversity and polarization diversity advantages of polarization MIMO radars, have good accuracy and do not require decoherence processing. However, there are still problems of low accuracy and large computational amount in the existing polarization MIMO radar array height measurement. Summary of the Invention

[0004] In view of the above problems, the present invention proposes a real-valued MUSIC height measurement method for meter-wave polarization MIMO radar based on matrix reconstruction, which further improves the estimation accuracy and reduces the computational amount based on the idea of matrix reconstruction and real-valued processing operations. To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0005] A real-valued MUSIC height measurement method for meter-wave polarization MIMO radar based on matrix reconstruction, characterized by comprising the following steps:

[0006] Step 1: Construct a height measurement model of a meter-wave polarization sensitive array. Assuming that the low elevation angle reflection region is a smooth and flat ground, the signal of the l-th snapshot reaching the target and the received signal data at the l-th snapshot can be obtained.

[0007] Step 2: Reconstruct the received signal vector data at the l-th snapshot to obtain a received signal matrix.

[0008] Step 3: Perform real-valued processing on the reconstructed received signal matrix using a unitary matrix and obtain the corresponding real-valued target elevation angle value.

[0009] Step 4: Calculate the target height according to the geometric relationship formula in the low elevation angle region to complete height measurement. Further, the specific operation steps of Step 1 include:

[0010] Step 101: Assume that the MIMO radar transmitted signal is a set of orthogonal signals where S m =[s m,1 ,...,s m,6 T , which satisfies the following formula:

[0011]

[0012] Then the signal of the l-th snapshot reaching the target is expressed as:

[0013] x(l)=[b t (θ d )+e -jδ ρ h b t (θ s )] T S (2)

[0014] where, is the phase difference caused by the wave path difference, R is the distance between the projection of the target on the ground and the projection of the radar on the ground, ρ h is the Fresnel reflection coefficient of the horizontally polarized wave, and its value is:

[0015]

[0016] where, ε is the surface complex dielectric constant, is the polarization transmitting array steering vector, and:

[0017] a(θ)=[1,exp(-jπsin(θ)),…,exp(-j(M - 1)πsin(θ))] T (4)

[0018] g(θ) is the polarization steering vector of a single electromagnetic vector sensor, and:

[0019]

[0020] where, θ represents θ d or θ s , γ∈[0,π / 2], η∈[-π,π] represent the polarization auxiliary angle and the polarization phase difference respectively, and φ is the azimuth angle;

[0021] Step 102: Let the azimuth angle φ = 90°, then the data of the l-th snapshot received by the entire array is expressed as:

[0022] ​X(l) = [b r (θ d ) + e -jδ ρ h b r (θ s )]ξ(l)[b t (θ d ) + e -jδ ρ h b t (θ s )] T S + N(l) (6)

[0023] where ξ(l) is the complex reflection coefficient, N(l) is the Gaussian white noise at the l-th snapshot, b r is the polarization receiving array steering vector, and b t is the polarization transmitting array steering vector;

[0024] Step 103: After performing matched filtering on Equation (6) using the transmitted signal, the received signal data expression at the l-th snapshot can be obtained as:

[0025] Y(l) = [b r (θ d ) + e -jδ ρ h b r (θ s )]ξ(l)[b t (θ d ) + e -jδ ρ h b t (θ s )] T + N(l)S H (l) (7)

[0026] Performing a vectorization operation on Equation (7) gives:

[0027]

[0028] Furthermore, the specific operation steps of Step 2 include:

[0029] Step 201: Reconstruct Equation (8) to obtain the received signal matrix Z(l) ∈ C MM×36 , which can be expressed as:

[0030] Z(l) = [Y 1,1 (l),..., Y 1,M (l), Y 2,1 (l),..., Y M,M (l)] (9)

[0031] where Ym,n $(l)\in\mathbb{C}$ 36×1 Represents the signal transmitted by the $m$-th polarization-sensitive array element and received by the $n$-th polarization-sensitive array element after being conducted through the air medium and reflected by the target;

[0032] Step 202: Expand Equation (9) into Equation (10):

[0033] $Z(l)=A\Lambda$ ξ $(l)G + V(l)=AD(l)+V(l)\ (10)$

[0034] where $D(l)=\Lambda$ ξ $(l)G$, $A$ is the steering vector after matrix reconstruction, $V(l)$ is the noise matrix of the reconstructed data, $G$ contains all polarization information of the received data, and $\Lambda$ ξ $(l)$ contains information such as reflection coefficients and wave path differences;

[0035] And:

[0036]

[0037]

[0038]

[0039] Furthermore, the specific operation steps of Step 3 include:

[0040] Step 301: Obtain the data of $L$ snapshots corresponding to Equation (10)

[0041] $Z$ L $=[Z(1),\cdots,Z(L)]\in\mathbb{C}$ MM×36L , and expand $Z$ L to obtain:

[0042]

[0043] where $\Pi$ N is a permutation matrix with elements on its anti-diagonal being 1 and elements in other positions being 0; Step 302: Process Equation (14) using a unitary matrix to obtain a real-valued matrix:

[0044]

[0045] where $(·)$ H denotes the conjugate transpose of the matrix, and $\Gamma$ K is a sparse unitary matrix, and its odd and even dimensions are defined respectively as:

[0046]

[0047] Step 303: Singular value decomposition of Equation (15) gives:

[0048]

[0049] where U s ∈ C MN×4 and U n ∈ C MN×MN-4 is composed of the left singular value vectors corresponding to 4 large singular values and the left singular value vectors corresponding to MN - 4 small singular values; Λ s and Λ n are composed of 4 large singular values and the remaining MN - 4 large singular values; V s ∈ C 72L ×4 and V n ∈ C 72L×MN-4 is composed of the right singular value vectors corresponding to 4 large singular values and the right singular value vectors corresponding to MN - 4 small singular values;

[0050] Step 304: Multiply Equation (15) on the right by V s to obtain such that the dimension of matrix Z R is reduced from 72L to 4, and is:

[0051]

[0052] Step 305: Obtain the covariance matrix of the real-valued data

[0053]

[0054] where denotes taking the conjugate transpose of matrix ;

[0055] Step 306: Perform eigenvalue decomposition on the real-valued matrix to obtain the signal subspace and the noise subspace:

[0056]

[0057] where the matrices E s and E n represent the signal subspace and the noise subspace respectively; Λ s and Λ n are the diagonal matrices composed of their eigenvalues;

[0058] Step 307: According to the orthogonality of the signal subspace and the noise subspace, the spectral peak search formula is obtained as:

[0059]

[0060] Among them, the steering vector

[0061] Step 308: According to the relationship between the direct wave direction θ d and the reflected wave direction θ s , reduce Equation (21) to a one-dimensional search, and the relationship between the direct wave direction θ d and the reflected wave direction θ s is as follows:

[0062] θ s = -arctan(tanθ d + 2h a / R) (22)

[0063] where h a is the reference element height and R is the target distance;

[0064] Step 309: Obtain the target elevation angle through one-dimensional spectrum peak search.

[0065] Furthermore, the formula for calculating the target height H described in Step 4 is:

[0066] H ≈ Rsinθ d + h a (23).

[0067] The beneficial effects of the present invention are:

[0068] The height measurement method based on meter-wave polarization MIMO radar proposed by the present invention makes full use of the waveform diversity and polarization diversity characteristics of the polarization MIMO radar. The received data matrix is reconstructed according to the height measurement model of the meter-wave polarization MIMO radar to eliminate the influence of multipath reflected echoes on height measurement. The reconstructed data matrix is processed into real values through a unitary matrix, effectively reducing the algorithm complexity; and the corresponding spectrum peak search formula is given, and this spectrum peak search formula does not require known polarization information. Finally, simulation experiments show that the method proposed by the present invention has better performance and still has considerable accuracy under low snapshots or low signal-to-noise ratios. Description of the Drawings

[0069] Figure 1 is the height measurement model diagram of the polarization MIMO radar;

[0070] Figure 2 is the ten-time spectrum peak search diagram;

[0071] Figure 3 is the diagram of the target angle estimation RMSE varying with the signal-to-noise ratio;

[0072] Figure 4 is the diagram of the target height estimation RMSE varying with the signal-to-noise ratio;

[0073] Figure 5 It is a graph showing the variation of complexity with the number of array elements. Specific implementation mode

[0074] In order to enable those of ordinary skill in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0075] I. Constructing a height measurement signal model for meter-wave polarized MIMO radar

[0076] The schematic diagram of the height measurement reflection model of the meter-wave polarized MIMO radar is as Figure 1 shown. Both the transmitting and receiving antennas are polarization-sensitive antennas placed vertically. The antennas are evenly placed and the element spacing d t = d r = λ / 2, where λ is the wavelength. In the figure, θ d is the direct wave angle, θ s is the reflection angle, h a is the reference element height, and h t is the target height.

[0077] Assume that the transmitted signal of the MIMO radar is a set of orthogonal signals where S m = [s m,1 ,..., s m,6 T , which satisfies the following formula:

[0078]

[0079] Assume that the low elevation reflection area is a smooth and flat ground. Then the signal of the l-th snapshot reaching the target can be expressed as:

[0080] x(l) = [b t (θ d ) + e -jδ ρ h b t (θ s )] T S (2)

[0081] where δ is the phase difference caused by the wave path difference and R is the distance between the projection of the target on the ground and the projection of the radar on the ground, and ρ h is the Fresnel reflection coefficient of the horizontally polarized wave:

[0082]

[0083] where ε is the surface complex dielectric constant, which can be determined by the relative dielectric constant ε r and the surface conductivity σ e ​Indication: ε = ε r -j60λσ e 。

[0084] is the polarization emission array steering vector, where:

[0085] a(θ) = [1, exp(-jπsin(θ)), …, exp(-j(M - 1)πsin(θ))] T (4)

[0086] where M represents the number of array elements, and j = (-1)^0.5 represents the imaginary unit of a complex number;

[0087] g(θ) is the polarization steering vector of a single electromagnetic vector sensor and can be expressed as:

[0088]

[0089] where θ can represent θ d or θ s , γ ∈ [0, π / 2] and η ∈ [-π, π] are the polarization auxiliary angle and the polarization phase difference respectively, φ is the azimuth angle. Since the present invention mainly considers elevation measurement, the azimuth angle φ is set to 90°.

[0090] Then the data of the l-th snapshot received by the entire array can be expressed as:

[0091] X(l) = [b r (θ d ) + e -jδ ρ h b r (θ s )]ξ(l)[b t (θ d ) + e -jδ ρ h b t (θ s )] T S + N(l) (6)

[0092] where ξ(l) is the complex reflection coefficient, b r is the polarization receiving array steering vector, b t is the polarization emission array steering vector, and N(l) is the Gaussian white noise at the l-th snapshot, whose mean is 0 and variance is σ 2 。

[0093] After performing matched filtering on Equation (6) using the transmitted signal, the following equation can be obtained:

[0094] Y(l) = [b r (θ d ) + e-jδ ρ h b r (θ s )]ξ(l)[b t (θ d )+e -jδ ρ h b t (θ s )] T +N(l)S H (l) (7)

[0095] Perform a vectorization operation on Equation (7) to obtain the vectorized data of the received data at the l-th snapshot:

[0096]

[0097] After matched filtering and vectorization operations, N is still Gaussian white noise.

[0098] II. Real-Valued MUSIC Altimetry Method Based on Matrix Reconstruction

[0099] (1) Principle of the Proposed Algorithm

[0100] To solve the influence of multipath reflected echo signals in the low elevation angle region of VHF MIMO radar on altimetry, reconstruct the received signal data expression (8) into a matrix Z(l)∈C MM×36 :

[0101] Z(l) = [Y 1,1 (l),...,Y 1,M (l),Y 2,1 (l),...,Y M,M (l)] (9)

[0102] where Y m,n (l)∈C 36×1 represents the signal transmitted by the m-th polarization-sensitive array element and received by the n-th polarization-sensitive array element after being conducted through the air medium and reflected by the target.

[0103] Equation (9) can be expanded as:

[0104] Z(l) = AΛ ξ (l)G + V(l) = AD(l) + V(l) (10)

[0105] where D(l) = Λ ξ (l)G, A is the steering vector after matrix reconstruction, V(l) is the noise matrix of the reconstructed data, G contains all polarization information of the received data, and Λ ξ (l) contains information such as reflection coefficients and wave path differences.

[0106]

[0107]

[0108]

[0109] It can be seen that the columns of G are linearly independent, and when ξ(l)≠0, R D = E(D(l)D(l) H ) has a rank of min(4, 36) = 4. In addition, it is worth noting that in Equation (10), when the rank of A is 4, the rank deficiency phenomenon caused by multipath coherent signals has been resolved, that is, the matrix reconstruction method eliminates the influence of multipath coherent signals. When there are K non-coherent low-altitude targets, the proposed method can solve the multipath coherent rank deficiency phenomenon of up to 36 / 4 non-coherent low-altitude targets.

[0110] However, the data in Equation (10) are complex-valued. Therefore, directly performing low elevation angle estimation will result in a large computational complexity. To reduce the algorithm complexity, the present invention uses a unitary matrix to perform real-valued processing on Equation (10) and derives the corresponding real-valued MUSIC elevation angle estimation method.

[0111] When the received data is L snapshots, the data expression of the corresponding L snapshots can be obtained from Equation (10) as Z L = [Z(1),..., Z(L)] ∈ C MM×36L . To make full use of the conjugate data, Z L can be extended as follows:

[0112]

[0113] where Π N is a permutation matrix with elements on its anti-diagonal being 1 and the rest being 0; it is easy to verify that Z L,U is a central Hermitian matrix. At this time, using a unitary matrix to process (14) can obtain a real-valued matrix:

[0114]

[0115] where (·) H denotes the conjugate transpose of the matrix, and Γ K is a sparse unitary matrix, whose odd and even dimensions are defined respectively as:

[0116]

[0117] When the number of received data snapshots is large, the huge computational load will increase the difficulty of practical applications. To reduce the dimension of the received data and the impact of noise on the data, singular value decomposition (SVD) is used to perform singular value decomposition on Equation (15), and we can get:

[0118]

[0119] Because there are four transmission paths in the low elevation angle region and the rank of the data covariance matrix after matrix reconstruction is 4, so U s ∈C MN×4 and U n ∈C MN×MN-4 are composed of the left singular value vectors corresponding to the 4 large singular values and the left singular value vectors corresponding to the MN - 4 small singular values. Λ s and Λ n are composed of 4 large singular values and the remaining MN - 4 large singular values. Similarly, V s ∈C 72L×4 and V n ∈C 72L×MN-4 are composed of the right singular value vectors corresponding to the 4 large singular values and the right singular value vectors corresponding to the MN - 4 small singular values. Multiply Equation (15) on the right by V s We can get the following equation:

[0120]

[0121] According to Equation (18), it is found that the dimension of matrix Z R is reduced from 72L to 4. When the number of snapshots L is large, it is not difficult to find that 72L >> 4. Therefore, it is not difficult to prove that the singular value technique can greatly reduce the matrix dimension.

[0122] Similarly, the covariance matrix of real-valued data can be obtained by the following equation:

[0123]

[0124] Among them, represents taking the conjugate transpose of matrix ;

[0125] For matrix performing eigenvalue decomposition, the following formula can be obtained:

[0126]

[0127] Matrices E s and E n represent the signal subspace and the noise subspace respectively, and their eigenvalues form diagonal matrices Λ s and Λ n .

[0128] Since is a real-valued matrix, E s and E n are both real-valued matrices. According to the orthogonality between the signal subspace and the noise subspace, the following spectral peak search formula can be derived:

[0129]

[0130] Since the received data is processed by the unitary matrix into real data, the steering vector for spectral peak search in Equation (21) is which does not contain any polarization parameters, wave path difference, and reflection coefficient information. Therefore, it is not difficult to prove that the proposed method can estimate the target elevation angle value without polarization information.

[0131] Equation (21) is for two-dimensional spectral peak search, which can be reduced to one-dimensional search according to the relationship between the direct wave direction and the reflected wave direction as follows:

[0132] θ s = -arctan(tanθ d + 2h a / R) (22)

[0133] Then, according to the target distance R and the estimated elevation angle value θ d , the target height H is calculated as:

[0134] H ≈ Rsinθ d + h a (23).

[0135] In summary, the algorithm proposed by the present invention mainly includes the following steps:

[0136] Step 1: Reconstruct the received signal vector using Equation (9);

[0137] Step 2: Perform real-valued processing on the reconstructed received signal matrix using the unitary matrix;

[0138] Step 3: Use the singular value technique to reduce the dimension of the received data and the influence of noise on the received data;

[0139] Step 4: Obtain the signal covariance matrix through Equation (19), and then perform eigenvalue decomposition on it to obtain the noise subspace matrix Ε n ;

[0140] Step 5: Perform spectral peak search through Equation (21) to obtain the target elevation angle;

[0141] Step 6: Obtain the target height according to the geometric relationship H ≈ R r sinθ d + h a in the low elevation angle region, Rr is the slant range between the target and the antenna.

[0142] Embodiment

[0143] To further illustrate the reliability and superiority of the algorithm proposed by the present invention, the algorithm is verified from the aspects of computational complexity and simulation experiments.

[0144] 1. Computational Complexity

[0145] From the above operation steps, the computational complexity of the method proposed by the present invention is divided into: 1) real-value processing; 2) estimating the real-value covariance matrix; 3) eigenvalue decomposition of the covariance; 4) spectral peak search. When evaluating the computational complexity, addition is ignored and only multiplication is considered. It is not difficult to find that one complex multiplication is equivalent to four real multiplications. The specific expressions of the complexity of each part are as follows:

[0146] 1) 24·72M 2 L;

[0147] 2) 72M 4 L;

[0148] 3) M 6 ;

[0149] 4) num·(8M 4 + 36M 2 )

[0150] As can be seen from the above, the complexity of the proposed algorithm is 36M 2 (48L + num) + M 4 (72L + 8num) + M 6 . The generalized MUSIC algorithm proposed in

[24] is abbreviated as the G-MUSIC algorithm, and its extended algorithm for polarimetric MIMO radar is the PG-MUSIC algorithm

[19] ; the maximum likelihood estimation height measurement method proposed in

[25] is abbreviated as the ML algorithm, and its extended algorithm for polarimetric MIMO radar is the P-ML

[21] . The complexity of the G-MUSIC algorithm is: 4M 4 L + 4M 6 + 4Θ(32M 2 + 8M 4 );

[0151] The complexity of the PG-MUSIC algorithm is 4(36M 2 ) 3 + 4(36M 2 ) 2 L + 4Θ(36·32M 2 + 8·36 2 M 4 );

[0152] The complexity of the ML algorithm is: 4M 4 (L + M 2 ) + 4Θ(32M 2 + 4M 4 + M 6 );

[0153] The complexity of the P-ML algorithm is:

[0154] 4·36 2 M 4 (L + 36M 2 ) + 4Θ(36 3 M 6 + 32·36M 2 + 4·36 2 M 4 )

[0155] where Θ is the number of spectral peak searches.

[0156] 2. Simulation Experiments

[0157] The algorithm proposed in the present invention is a low-elevation height measurement algorithm. Therefore, the angle search range is set to 0.5° - 12°, and the search interval is 0.01°. From this, the number of searches Θ = 1151 can be obtained. Assume a monostatic meter-wave polarized MIMO radar system with the number of transmitting and receiving array elements M = N = 6, d t = d r = λ / 2, the wavelength λ = 1, the array element height h a = 5m, and the number of Monte Carlo experiments K = 500. In the simulation experiment, the number of low-altitude targets is set to 1, and the root mean square error formula is defined as:

[0158]

[0159]

[0160] where is the elevation angle value estimated in the k-th experiment, is the target height estimated in the k-th experiment, and K is the number of Monte Carlo experiments.

[0161] (1) Experiment 1

[0162] In Experiment 1, let the number of snapshots L = 10, the actual elevation angle of the target be 3°, and SNR = 10dB. Attached Figure 2 is the spectral peak search graph of the proposed method for ten times. From Figure 2 it can be seen that the proposed method can correctly measure the target elevation angle information, verifying the correctness of the method proposed in the present invention.

[0163] (2) Experiment 2

[0164] In Experiment 2, the number of snapshots \(L = 10\), the actual elevation angle of the target is \(3^{\circ}\), the distance \(R\) between the target and the radar is \(200\ km\), and the signal-to-noise ratio ranges from \(-10\ dB\) to \(10\ dB\). Attached Figure 3 shows the relationship between the root mean square error of target elevation angle estimation and the signal-to-noise ratio of five algorithms. Attached Figure 4 shows the relationship between the root mean square error of target height estimation and the signal-to-noise ratio of five algorithms. From Figure 3 and Figure 4 it can be seen that the accuracies of the PG-MUSIC and P-ML methods are better than those of the G-MUSIC and ML methods, which proves the polarization diversity advantage of the polarization-sensitive array. In addition, on the premise of the same polarization radar, the accuracy of the algorithm proposed in the present invention is better than that of the PG-MUSIC and P-ML methods, thus proving the superiority of this algorithm.

[0165] (3) Experiment 3

[0166] In Experiment 3, attached Figure 5 shows the relationship between the computational complexity of five algorithms and the number of array elements. From Figure 5 it can be seen that the computational complexities of the PG-MUSIC and P-ML methods are significantly higher than those of the G-MUSIC and ML methods. This shows that although the polarization MIMO radar has the polarization diversity advantage, it will also increase the computational complexity of the algorithm. It is worth noting that the computational complexity of the proposed algorithm is the lowest, because the proposed algorithm performs real-value processing on the data, and in addition, the dimension of the steering vector for spectral peak search in the proposed method is also lower than that of the PG-MUSIC and P-ML methods. This proves that the proposed method is more conducive to engineering implementation. In addition, according to the experimental results of this experiment and Experiment 2, it can be found that compared with the other four algorithms, the algorithm proposed in this paper improves the measurement accuracies of the target elevation angle and height while reducing the computational complexity of the algorithm.

[0167] Literature

[19] Tan J, Nie Z. Polarization Smoothing Generalized MUSIC algorithm with PSA monostatic MIMO radar for low angle estimation[J]. Electronics Letters, 2018, 54(8): 527 - 529.

[0168] Reference

[21] G. Zheng, Y. Song, C. Chen. Height Measurement for with wave polarimetric MIMO radar: signal model and MUSIC algorithm. Signal Processing, Vol. 190, Jan. 2022, 108344。

[0169] Reference

[24] Haimovich A M, Blum R S, Cimini L J. MIMO Radar with Widely Separated Antennas[J]. IEEE Signal Processing Magazine, 2007, 25(1): 116 - 129.。

[0170]

[25] D. Rahamim, J. Tabrikian, R. Shavit. Source localization using vector sensor array in a multipath environment[J]. IEEE Transactions on Signal Processing, 2004, 52(11): 3096–3103。

[0171] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A real - valued MUSIC height measurement method for meter - wave polarization MIMO radar based on matrix reconstruction, characterized in that, it includes the following steps: Step 1: Construct a height measurement model for the meter - wave polarization sensitive array. Assuming that the low - elevation reflection area is a smooth and flat ground, the signal of the l - th snapshot reaching the target and the received signal data at the l - th snapshot can be obtained; Step 2: Reconstruct the received signal vector data at the l - th snapshot to obtain the received signal matrix; Step 3: Use the unitary matrix to perform real - valued processing on the reconstructed received signal matrix and obtain the corresponding real - valued target elevation angle value; Step 4: Calculate the target height according to the geometric relationship formula in the low - elevation area to complete the height measurement.

2. The real - valued MUSIC height measurement method for meter - wave polarization MIMO radar based on matrix reconstruction as claimed in claim 1, characterized in that, the specific operation steps of Step 1 include: Step 101: Assume that the transmitted signal of the MIMO radar is a set of orthogonal signals where S m =[s m,1 ,..., s m,6 T , which satisfies the following equation:​ The signal of the l - th snapshot reaching the target is expressed as: x(l) = [b t (θ d ) + e -jδ ρ h b t (θ s )] T S (2) Among them, is the phase difference caused by the wave path difference, R is the distance between the projection of the target on the ground and the projection of the radar on the ground, and ρ h is the Fresnel reflection coefficient of the horizontally polarized wave, and its value is: where ε is the surface complex permittivity, is the polarization emission array steering vector, and: a(θ) = [1, exp(-jπsin(θ)), …, exp(-j(M - 1)πsin(θ))] T (4) g(θ) is the polarization steering vector of a single electromagnetic vector sensor, and: where θ represents θ d or θ s , γ ∈ [0, π / 2], η ∈ [-π, π] represent the polarization auxiliary angle and the polarization phase difference respectively, and φ is the azimuth angle; Step 102: Let the azimuth angle φ = 90°, then the data of the l - th snapshot received by the entire array is expressed as: X(l) = [b r (θ d ) + e -jδ ρ h b r (θ s )]ξ(l)[b t (θ d ) + e -jδ ρ h b t (θ s )] T S + N(l) (6) where, ξ(l) is the complex reflection coefficient, N(l) is the Gaussian white noise at the l-th snapshot, b r is the polarization receiving array steering vector, b t is the polarization transmitting array steering vector; Step 103: After performing matched filtering on Equation (6) using the transmitted signal, the expression of the received signal data at the l - th snapshot can be obtained: Y(l) = [b r (θ d ) + e -jδ ρ h b r (θ s )]ξ(l)[b t (θ d ) + e -jδ ρ h b t (θ s )] T + N(l)S H (l) (7) Perform vectorization operation on Equation (7) to get:

3. The real - valued MUSIC height measurement method for meter - wave polarization MIMO radar based on matrix reconstruction as claimed in claim 2, characterized in that, the specific operation steps of Step 2 include: Step 201: Reconstruct Equation (8) to obtain the received signal matrix \(Z(l)\in\mathbb{C}\) MM×36 , which can be expressed as: Z(l) = [Y 1,1 (l),...,Y 1,M (l),Y 2,1 (l),...,Y M,M (l)] (9) where Y m,n (l) ∈ C 36×1 represents the signal transmitted by the m-th polarization-sensitive array element and received by the n-th polarization-sensitive array element after being conducted through the air medium and reflected by the target; Step 202: Expand Equation (9) into Equation (10): Z(l) = AΛ ξ (l)G + V(l) = AD(l) + V(l) (10) where \(D(l)=\Lambda\) ξ (l)G, A is the steering vector after matrix reconstruction, \(V(l)\) is the noise matrix of the reconstructed data, G contains all polarization information of the received data, \(\Lambda\) ξ (l) contains information such as reflection coefficient and wave path difference; and:

4. The real - valued MUSIC height measurement method for meter - wave polarization MIMO radar based on matrix reconstruction as claimed in claim 3, characterized in that, the specific operation steps of Step 3 include: Step 301: Use Equation (10) to obtain the data of the corresponding L snapshots Z L = [Z(1),..., Z(L)] ∈ C MM×36L and expanding Z L gives: Among them, Π N is a switching matrix, the elements on its anti-diagonal are 1, and the elements in the remaining positions are 0; Step 302: Processing Equation (14) with a unitary matrix can obtain a real-valued matrix: where (·) H denotes the conjugate transpose of a matrix, and Γ K is a sparse unitary matrix, and its odd and even dimensions are defined as follows: Step 303: Perform singular value decomposition on Equation (15) to get: Z R = U s Λ s V s H + U n Λ n V n H ∈ C MM×72L (17) where U s ∈ C MN×4 and U n ∈ C MN×MN-4 is composed of the left singular value vectors corresponding to 4 large singular values and the left singular value vectors corresponding to MN - 4 small singular values; Λ s and Λ n is composed of 4 large singular values and the remaining MN - 4 large singular values; V s ∈ C 72L×4 and V n ∈ C 72L×MN-4 is composed of the right singular value vectors corresponding to 4 large singular values and the right singular value vectors corresponding to MN - 4 small singular values; Step 304: Right-multiply the formula (15) by V s to obtain Let the matrix Z R reduce its dimension from 72L to 4, and be: Step 305: Obtain the covariance matrix of the real-valued data Among them, denotes taking the conjugate transpose of the matrix ; Step 306: Perform eigenvalue decomposition on the real-valued matrix to obtain the signal subspace and the noise subspace: Among them, matrix E s and E n represent the signal subspace and the noise subspace respectively; Λ s and Λ n is a diagonal matrix composed of its eigenvalues; Step 307: According to the orthogonality of the signal subspace and the noise subspace, the spectrum peak search formula is obtained as: Among them, the steering vector Step 308: Reduce Equation (21) to a one-dimensional search according to the relationship between the direct wave direction θ d and the reflected wave direction θ s , and the relationship between the direct wave direction θ d and the reflected wave direction θ s is as follows: θ s = -arctan(tanθ d + 2h a / R) (22) where h a is the reference element height, and R is the target distance; Step 309: Obtain the target elevation angle through one - dimensional spectrum peak search.

5. The real - valued MUSIC height measurement method for meter - wave polarization MIMO radar based on matrix reconstruction as claimed in claim 4, characterized in that, the formula for calculating the target height H in Step 4 is: H≈Rsinθ d +h a (23).

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